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The \(nth\) term (\(t_n\)) of a certain sequence is defined as \(t_n=t_{n-1}+4\). If...

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Re: The \(nth\) term (\(t_n\)) of a certain sequence is defined as \(t_n=t_{n-1}+4\). If...

by Brent@GMATPrepNow » Tue Mar 03, 2020 6:20 am
BTGmoderatorLU wrote: ↑
Tue Mar 03, 2020 2:58 am
 Source: Magoosh

The \(nth\) term (\(t_n\)) of a certain sequence is defined as \(t_n=t_{n-1}+4\). If \(t_1=-7\) then \(t_{71}=\)

A. 273
B. 277
C. 281
D. 283
E. 287

The OA is A
If we don't already know the formula for arithmetic sequences, we can still answer the question.

The given formula tells us that each term in the sequence is 4 greater than the term before it.
So, let's list some terms to see if we can see a pattern

term1 = -7
term2 = -7 + 4
term3 = -7 + 4 + 4
term4 = -7 + 4 + 4 + 4
term5 = -7 + 4 + 4 + 4 + 4
.
.
.
At this point we can probably see the pattern

So, term71 = -7 + 4 + 4 + 4 + 4 + 4 + 4 + 4.......

QUESTION: How many 4's are in the sum for term71?
Well, term1 has 0 4's
term2 has 1 4
term3 has 2 4's
term4 has 3 4's
etc

So, we can see that term71 has 70 4's

In other words, term71 = -7 + (70)(4)
= -7 + 280
= 273

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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